Abstract
For a unital ring R R , R C F M α ( R ) \mathrm {RCFM}_\alpha (R) denotes the ring of row and column finite matrices over R R indexed by α \alpha . We give necessary and sufficient structural conditions on R C F M α ( R ) \mathrm {RCFM}_\alpha (R) which are equivalent to R R being, respectively, Quasi-Frobenius, left artinian, and left noetherian.
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